# How do you write the equation of the line given the slope and a point on the line m = -4, point (2, -5)?

##### 1 Answer
May 25, 2017

See a solution process below:

#### Explanation:

We can use the point-slope formula to write an equation for this problem. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the slope and the values from the point in the problem gives:

$\left(y - \textcolor{red}{- 5}\right) = \textcolor{b l u e}{- 4} \left(x - \textcolor{red}{2}\right)$

$\left(y + \textcolor{red}{5}\right) = \textcolor{b l u e}{- 4} \left(x - \textcolor{red}{2}\right)$

We can also solve for $y$ to put the equation in slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

$y + \textcolor{red}{5} = \left(\textcolor{b l u e}{- 4} \times x\right) - \left(\textcolor{b l u e}{- 4} \times \textcolor{red}{2}\right)$

$y + \textcolor{red}{5} = - 4 x - \left(- 8\right)$

$y + \textcolor{red}{5} = - 4 x + 8$

$y + \textcolor{red}{5} - 5 = - 4 x + 8 - 5$

$y + 0 = - 4 x + 3$

$y = \textcolor{red}{- 4} x + \textcolor{b l u e}{3}$